Question

A corporate bond with a coupon rate of 6% has been issued at a price of K102.50 and k100.00 nominal and it is redeemable at its par value of K100.00 at the end of year 5. the bond pays coupon interest annually.

Reguired

Calculate the bonds yield to maturity

calculate the bonds macaulay duration and state the impact of the bonds price of an increase in interest rates by 50 basis points

Answer 1

K = N

Bond Price =∑ [( Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =5

102.5 =∑ [(6*100/100)/(1 + YTM/100)^k]     +   100/(1 + YTM/100)^5

k=1

YTM% = 5.42

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($102.50)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	6.00	1.05	5.69	5.69
2	6.00	1.11	5.40	10.80
3	6.00	1.17	5.12	15.36
4	6.00	1.24	4.86	19.43
5	106.00	1.30	81.41	407.06
			Total	458.35

.

Macaulay duration =(∑ Duration calc)/(bond price*number of coupon per year)

=458.35/(102.5*1)

=4.471684

Modified duration = Macaulay duration/(1+YTM)

=4.47/(1+0.0542)

=4.241779

Using only modified duration

Mod.duration prediction = -Mod. Duration*Yield_Change*Bond_Price

=-4.24*0.005*102.5

=-2.17

%age change in bond price=Mod.duration prediction/bond price

=-2.17/102.5

=-2.12%

New bond price = bond price+Modified duration prediction

=102.5-2.17

=100.33